3D particle positioning by using the Fraunhofer criterion

In particle tracking velocimetry, the necessary information is the 3D location of a given particle in space. This information can be obtained by examining the real image or by analyzing the interference fringe recorded on a digital camera. In this work, we measure the three-dimensional position of spherical particles by calculating the Central Spot Size of the interference pattern of a particle diffraction image. The Central Spot Size is obtained by combining the Continuous Wavelet transform and circle Hough transform. The Continuous Wavelet transform allow us in only one step enhanced quality of particle images and sets a threshold to select properly places where a Central Spot Size appear in order to determine its size via the Hough transform. The size and centroid of the Central Spot Size render z and x–y position of a particle image, respectively. The Central Spot Size is related to a criterion of a simplified theory given by the Fraunhofer theory in order to obtain z particle position. Our approach has been applied to simulated and experimental particle images. Simulated particle images show good agreement between actual and calculated Central Spot Size. An average relative error of 0.5% and 1.12% for x–y and z directions, respectively, was found in the analysis. Our experimental particle images were obtained from particle motion inside a channel. The quality of the particle images determines the accuracy of the calculation of the Central Spot Size of a particle image.

Research highlights
► We presented a procedure to determine 3D particle position for tracking applications.
► The procedure is based in the determination of the CSS of a particle image via the CWT and CHT.
► The CWT enhances the quality of particle images and sets a threshold in only one step.
► We relate the CSS to a criterion obtained by the Fraunhofer diffraction theory.
► Knowledge of this criterion enables us to handle less complicated formulas to save time in numerical computations.